US 7815809 B2 Abstract A method for conductivity calculation in a treatment fluid downstream a filtration unit in a blood treatment apparatus is provided. The conductivity calculation is then used for clearance and fistula flow determination. A flow of treatment fluid is created in the filtration unit; a change in the conductivity of the treatment fluid at the inlet of the filtration unit is imposed to cause an induced conductivity change in the fluid at the outlet of the filtration unit; a predetermined number of conductivity values Cdo downstream from the filtration unit are measured. The measured conductivity values define a curve the pattern of which is estimated by means of one interpolating mathematical function in an interval of time after the occurrence of the induced conductivity change; a characteristic measuring time tcalc
_{clr }is determined. The value of the interpolating mathematical function at the characteristic measuring time tcalc_{clr }represents the conductivity value Cdo2 of the treatment fluid downstream from the filtration unit after the induced conductivity change.Claims(78) 1. A method for determining a conductivity of a treatment fluid downstream from a filtration unit in a blood processing machine, said unit comprising a first compartment for the circulation of blood and a second compartment for the circulation of the treatment fluid, said second compartment being separated from the first compartment by interposing at least a semi-permeable membrane; said method comprising the steps of:
creating a flow of blood through the first compartment of the filtration unit;
creating a flow of treatment fluid through the second compartment of the filtration unit;
imposing, for a predetermined time interval, a change in the conductivity of the treatment fluid at an inlet of the filtration unit to cause an induced conductivity change in the fluid at an outlet of said filtration unit;
measuring a predetermined number of conductivity values Cdo downstream from the filtration unit, said conductivity values Cdo defining a downstream conductivity curve;
defining at least one interpolating mathematical function for estimating a pattern of said downstream conductivity curve in an interval of time after causing the induced conductivity change;
wherein the mathematical function has the form:
Cdo_ln_{cir} =Cdi _{step,mean}−sign*exp(c(1)*t+c(2))where c(1) and c(2) are coefficients derived from the least squares interpolation of the mathematical function and Cdi
_{step,mean}=an inlet conductivity value after the change in conductivity;determining a characteristic measuring time tCalc
_{clr}, wherein said determination of said characteristic measuring time tCalc_{clr }comprises the sub steps of estimating an intermediate time tA_{clr }representative of a transient due to the induced conductivity change in the fluid, and correcting the intermediate time tA_{clr }through an addition of a second time term tcbf, which is a function of the blood flow; andcalculating by means of a control unit a value of the interpolating mathematical function at said characteristic measuring time tCalc
_{clr}, said value representing a conductivity value Cdo2 of the fluid downstream from the filtration unit after the induced conductivity change, wherein the determination of the characteristic measuring time tcalc_{clr }comprises the following sub steps:
estimation of the intermediate time tA
_{clr }representative of a transient due to the induced conductivity change in the fluid, said time tA_{clr }depending on at least a filtration unit volume, blood and treatment fluid flows, and the change in the conductivity of the treatment fluid at the inlet of the filtration unit, andcorrection of the intermediate time tA
_{clr }through the addition of the second time term tcbf, which is a function of blood flow rate, tcalc_{clr }being defined as tcalc_{clr}=tA_{clr}+tcbf, the Cdo2 value being the value of the equation at t=tcalc_{clr}.2. A method according to
3. A method according to
_{clr }is calculated using the equation: tCalc_{clr}=tA_{clr}+tcbf, where tcbf=16/60+260/Qb, Qb being the blood flowrate.4. A method according to
_{clr }is calculated using the function: unit_f=ln(sign*(Cdi_{step,set}−Cdo)/potential), where potential=Cdi_{step,mean}−Cdo_{pre,mean}, and by performing an interpolation with a least squares estimation on the data of the area falling between said function and the x-coordinate time axis in a predetermined time interval, said intermediate time tA_{clr }coinciding with the instant at which the interpolating function intersects the x-coordinate time axis.5. A method according to
6. A method according to
measuring a predetermined number of conductivity values upstream from the filtration unit, said conductivity values defining an upstream conductivity curve;
determining a characteristic time t0
_{Cdo }of the downstream conductivity curve;determining a characteristic time t0
_{Cdi }of the upstream conductivity curve;synchronizing said downstream and upstream conductivity curves on the basis of the characteristic time of the downstream conductivity curve t0
_{Cdo }and the characteristic time of the upstream conductivity curve t0_{Cdi}, to enable comparison of the respective conductivity values; andcomparing the downstream and upstream conductivity curves after the conductivity curves have been synchronized to determine one or more downstream conductivity values.
7. A method according to
_{Cdi }of the upstream conductivity curve coincides with the instant at which the change in conductivity occurs in the upstream conductivity curve, the characteristic time t0_{Cdo }of the downstream conductivity curve corresponding to the instant at which the induced conductivity change downstream from the filtration unit occurs.8. A method according to
_{Cdi }of the upstream conductivity curve is calculated by estimating an area defined below the upstream conductivity curve, the characteristic time t0_{Cdi }coinciding with the instant at which the area under the upstream conductivity curve takes on an average value greater than a predetermined threshold.9. A method according to
_{Cdo }of the downstream conductivity curve comprises a further step of making a preliminary estimate of the value of the characteristic time t0_{Cdo }and subsequently correcting the preliminary estimate if incorrect.10. A method according to
_{pre,mean }prior to the effects of the change in conductivity, said determination being made on the basis of an average of the measured conductivity values Cdo prior to the effects of the change; comparing the measured conductivity values at the outlet of the filtration unit Cdo with the average outlet conductivity value Cdo_{pre,mean}; estimating the instant at which the measured conductivity values Cdo appear constantly greater than the average outlet conductivity value Cdo_{pre,mean}.11. A method according to
_{pre,mean }a number of times, causing the preliminary estimate of the characteristic time t0_{Cdo }of the downstream conductivity curve to coincide with the instant of the last condition in which the measured conductivity values Cdo are greater than the average outlet conductivity value Cdo_{pre,mean}.12. A method according to
_{Cdo }value of the downstream conductivity curve comprises the following sub steps: creating an appropriate mathematical expression unit_f, which is a function of the conductivity values measured downstream from the filtration unit Cdo, and of the known change in the conductivity of the inlet fluid, Cdi_{step,set}, said expression being normalized if necessary; and, performing a least squares estimation of said expression unit_f in a predetermined time interval.13. A method according to
_{step,set}−Cdo)/potential)), where potential=Cdi_{step,set}−Cdo_{pre,mean}; Cdi_{step,set}=value of the known change in conductivity at the filtration unit inlet; Cdo=conductivity values measured downstream from the filtration unit; Cdi_{step,mean}=inlet conductivity value after the change in conductivity, and Cdo_{pre,mean}=average outlet conductivity value prior to the change in conductivity.14. A method according to
_{—}1n_{clr}=Cdi_{step,set}−sign*(exp(c_{clr}(1)*t+c_{clr}(2))), where c_{clr}(1) and c_{clr}(2) are coefficients derived from the least squares interpolation of the mathematical expression unit_f.15. A method according to
_{clr}(1) and c_{clr}(2) derived from the previous least squares interpolation, and a function of the known change in conductivity Cdi_{step,set }of the inlet fluid and a function of the conductivity values downstream from the filtration unit Cdo, said mathematical function f_norm being normalized if necessary; and, performing a least squares interpolation on the mathematical function f_norm within a predetermined interval of values.16. A method according to
_{clr}(1) and c_{clr}(2) derived from the previous least squares interpolation, and a function of the known change in conductivity Cdi_{step,set }of Cdi the inlet fluid and a function of the conductivity values downstream from the filtration unit Cdo, said mathematical function f_norm being normalized if necessary; and, performing a least squares interpolation on the mathematical function f_norm within a predetermined interval of values, wherein the mathematical function used is calculated using the following equation: f_norm=(f2_{clr}−min(f2_{clr}))/max(f2_{clr}−min(f2_{clr})), where f2cir=Cdo_{—}1n_{clr}−Cdo.17. A method according to
_{clr}(3) and c_{clr}(4) derived from the least squares interpolation of the mathematical function.18. A method according to
19. A method according to
_{Cdo }of the characteristic time of the downstream conductivity curve coincides with the instant at which the mathematical estimation function f_norm_est takes on a value of 1.0.20. A method according to
_{clr}(3)*t+c_{clr}(4)), where c_{clr}(3) and c_{clr}(4) are a coefficients derived from the least squares interpolation of the natural logarithm of the mathematical function f_norm.21. A method according to
_{Cdo }is obtained using the following formula: t0_{Cdo}=−c_{clr}(4)/c_{clr}(3).22. A method according to
23. A method according to
_{Cdi }and t0_{Cdo }determined by the upstream and downstream curves.24. A method according to
_{step,mean}, said determination being based on an average of the measured conductivity values Cdi after the effects of the imposed change in conductivity.25. A method according to
_{step,mean }fall within a time interval between an instant at which a change in conductivity occurs in an upstream conductivity curve, t0_{Cdi}+3 minutes, and an instant at which the effects of a change in conductivity cease in the same curve, tf_{Cdi}−1 minute.26. A method according to
_{Cdi}, at which the effects of the change in conductivity cease in an upstream conductivity curve, is calculated by estimating an area defined below the upstream conductivity curve, said instant tf_{Cdi }being identified by the moment at which the area under the upstream conductivity curve takes on an average value below a predetermined threshold.27. A method according to
28. A method according to
29. A method according to
30. A method according to
_{filt,i}=(N−1)/N*Cdi_{filt,i}−1+1/N*Cdii−1, where N=filtering factor.31. A method according to
32. A method according to
33. A method according to
_{filt }measured upstream.34. A method according to
_{corr}=Cdo+(Cdo2−Cdo_{pre,mean})*Cdi_{diff}/step size, where Cdi_{diff}=Cdi_{filt}−Cdi_{step,mean}; step size=Cdi_{pre,mean}−Cdi_{step,mean}; Cdo2=conductivity value downstream from the filtration unit after the effects of the change in conductivity.35. A method according to
_{corr}=Cdo+(Cdo2−Cdo_{pre,mean})*Cdi_{diff}/step size, where Cdi_{diff}=Cdi_{filt}−Cdi_{step,mean}; step size=Cdi_{pre,mean}−Cdi_{step,mean}, Cdo2=conductivity value downstream from the filtration unit after the effects of the change in conductivity; and wherein, for the purpose of calculating Cdo_{corr}, a preliminary estimate value of Cdo2 is used, said estimate being defined by the value that the function Cdo_{—}1n_{clr }assumes at the instant t=t0_{Cdo}.36. A method according to
37. A method according to
_{target}, which is a function of the conductivity curve, and a second term tcbf, which is a function of the blood flow.38. A method according to
39. A method according to
_{target}, which is a function of the conductivity curve, and a second term tcbf, which is a function of the blood flow, the determination of the first term t_{target }for calculating the characteristic time entailing the sub steps of: estimating an intermediate time tA_{clr}, deriving the first term t_{target}, said first term t_{target }coinciding with the time that makes a straight line passing through points (t0_{Cdo}; Cdo0) and (tA_{clr}; Cd0A) take on the value Cdo_{pre,mean}+step size, where Cdo0 and CdoA are the values taken on by curve Cdo at instants t0_{Cdo }and tA_{clr }where Cdo_{pre,mean }is the average outlet conductivity prior to the effects of the change in conductivity.40. A method according to
_{clr }is calculated using the function: unit_f=ln(sign*(Cdi_{step,set}−Cdo)/potential), and performing an interpolation with a least squares estimation on the data of the area between said function and the time axis of the x-coordinates in a predetermined interval of time, said intermediate time tA_{clr }coinciding with the instant at which the interpolating function intersects the time axis, thereby taking on a value of zero.41. A method according to
42. A method according to
43. A method according to
_{step,mean }and Cdo_{corr}, in a predetermined time interval.44. A method according to
_{step,mean}−Cdo_{corr})).45. A method according to
_{clr }and tstartCF_{clr}+1.5 min.46. A method according to
_{—}1n_{clr}, which is a function of Cdi_{step,mean }and c(1) and c(2), where c(1) and c(2)=coefficients derived from the least squares interpolation of function f.47. A method of calculating the filter clearance by means of a function relation of Cdo2, Cdo1, Cdi2 and Cdi1, said conductivities being calculated using the method according to
48. A method according to
where Cdi2=Cdi
_{step,mean }or Cdi_{set,step}, Cdi1=Cdi_{pre,mean }or Cdi_{set,pre}, Cdo1=Cdo_{pre}(t=tCalc_{clr}), Qd=flow of dialysate fluid, QUF=ultra filtration flow of dialysate fluids.49. A method for calculating fistula flow, comprising the steps of: determining a filter clearance according to the method of
50. A method according to
51. A method according to
where Hct is the hematocrit, Tp is the total plasma protein content and Fr is the red cell water fraction=volume water in red cells/total volume of red cells.
52. A method according to
_{step,set }and Cdo.53. A method according to
54. A method according to
_{step,set}−Cdo)).55. A method according to
_{step,mean}, and c_{pre,acc}(1) and c_{pre,acc}(2), where c_{pre,acc}(1) and c_{pre,acc}(2) are coefficients of the least squares interpolation performed on the second function f.56. A method according to
_{pre,acc}=Cdi_{step,mean}−sign*exp(c_{pre,acc}(1)*t+c_{pre,acc}(2)).57. A method according to
_{crl }and t=t0_{acc}−[˝] min.58. A method according to
_{pre,acc }at the instant t=tCalc_{acc}.59. A method according to
_{step,set }or Cdi_{step,mean }and Cdo.60. A method according to
61. A method according to
_{step,set}−Cdo)) or f=ln(sign*(Cdi_{step,mean}−Cdo)).62. A method according to
_{step,mean}, c_{acc}(1), and c_{acc}(2), where c_{acc}(1) and c_{acc}(2) are coefficients of the least squares interpolation performed on the second relation f.63. A method according to
_{acc}=Cdi_{step,mean}−sign*(exp(c_{acc}(1)*t+c_{acc}(2))).64. A method according to
_{acc }and t=tfcCdi−1 minute.65. A method according to
_{pre,acc }at the instant t=tCalc_{acc}.66. A method according to
67. A method according to
_{acc }comprises the following steps: filtering the current downstream conductivity curves; creating a mathematical relation f_flt, which is a function of Cdi_{step,mean }and Cdo_flt; and, performing a least squares interpolation of said function in an established time interval.68. A method according to
_{acc }additionally comprises the steps of: creating a relation Cdo_{—}1n_{acc,est}, which is a function of Cdi_{step,mean}, c_{acc,est}(1), and c_{acc,est}(2), c_{accest}(1) and c_{acc,est}(2) being coefficients derived from the interpolation of the mathematical relation f_flt; and, constructing a further relation f<2> acc, which is the difference between Cdo_{—}1n_{acc,est }and Cdo_flt.69. A method according to
_{acc }comprises the further sub steps of creating a difference function diff_f2_{acc}=f2_{acc}(i)−f2_{acc}(i−1) and standardizing said difference function, if necessary, to obtain the function: f2_{der} _{ — } _{norm}=diff2_{acc}/min(diff−f2_{acc}).70. A method according to
_{acc,est }is the instant at which f2_{der} _{ — } _{norm }first takes on a value greater than 0.5, t0_{acc }preferably being defined as t0_{acc}=t0_{acc,est}−0.1 min.71. A method according to
_{acc }coincides with tCalc_{acc}.72. A method according to
_{der} _{ — } _{norm}, after peaking, falls below the value of 0.2, plus an increment of 0.5 min.73. A method of determining the conductivity of a process fluid downstream from a filtration unit in blood processing machines, said unit comprising a first compartment for the circulation of blood and a second compartment for the circulation of the process fluid, said method comprising the following steps:
creating a flow of fluid through the second compartment of a filtration unit;
imposing, for a predetermined time interval, a change in the conductivity of the process fluid at the inlet of the filtration unit in order to cause an induced conductivity change at the outlet;
measuring a predetermined number of conductivity values upstream and downstream from the filtration unit defining respectively upstream and downstream conductivity curves,
determining, by means of a control unit making mathematical calculations, at least a characteristic time t0
_{Cdi }of the upstream conductivity curve;determining, by means of a control unit making mathematical calculations, a corresponding preliminary estimate of a characteristic time t0
_{Cdo }of the downstream conductivity curve, the preliminary estimate of the characteristic time t0_{Cdo }of the downstream conductivity curve corresponding to the instant at which the induced conductivity change downstream from the filtration unit occurs, said preliminary estimate comprising the following sub-steps:
a) determining the average conductivity at the outlet of the filtration unit Cdo
_{pre,mean }prior to the effects of the change in conductivity, said determination being made on the basis of an average of the measured conductivity values Cdo prior to the effects of the change;b) comparing the measured conductivity values at the outlet of the filtration unit Cdo with the previously determined average outlet conductivity value Cdo
_{pre,mean};c) estimating the instant at which the measured conductivity values Cdo appear constantly different than the previously calculated average outlet conductivity value Cdo
_{pre,mean};correcting the preliminary estimate of the characteristic time t0
_{Cdo }value of the conductivity curve downstream from the filtration unit comprising:
a) creating a mathematical expression unit_f, which is a function of the conductivity values measured downstream from the filtration unit Cdo, and of the known change in the conductivity of the inlet fluid; the mathematical expression used being the following:
unit _{—} f=ln(sign*(Cdi _{step,set} −Cdo)/potential))where potential=Cdi
_{step,mean}−Cdo_{pre,mean};where Cdi
_{step,set}=a value of the known change in conductivity at the filtration unit inlet;where Cdo=conductivity values measured downstream from the filtration unit;
where Cdi
_{step,mean}=inlet conductivity value after the change in conductivity;where Cdo
_{pre,mean}=average outlet conductivity value prior to the change in conductivity; andperforming a least squares estimation of said expression unit_f in a predetermined time interval;
b) performing a least squares interpolation on said mathematical expression unit_f in a predetermined time interval; the least squares estimation being performed on the mathematical expression unit_f and the estimate being called
Cdo _{—}1n _{clr} =Cdi _{set,step}−sign*exp(c _{clr}(1)*t+c _{clr}(2))where c
_{clr}(1) and c_{clr}(2) are coefficients derived from the least squares interpolation of the mathematical expression unit_f;c) creating a mathematical function f_norm, which is a function of coefficients c
_{clr}(1) and c_{clr}(2) derived from the previous least squares interpolation, a function of the known change in conductivity Cdi_{step,set }of the inlet fluid and a function of the conductivity values downstream from the filtration unit Cdo, the mathematical function used being the following:
f_norm=(f2_{clr}−min*(f2_{clr}))/max(f2_{clr}−min(f2_{clr}))where f2
_{clr}=Cdo_{—}1n_{clr}−Cdod) performing a least squares interpolation on the mathematical function f_norm within a predetermined interval of values,
e) creating a mathematical estimation function f_norm_est, which is a function of the coefficients c
_{clr}(3) and c_{clr}(4) derived from the least squares interpolation of the mathematical function, the mathematical estimation function used being the following:
f_norm_est=exp(c _{clr}(3)*t+c _{clr}(4))where c
_{clr}(3) and c_{clr}(4) are the coefficients derived from the least squares interpolation of the natural logarithm of the mathematical function f_norm; the corrected value t0_{Cdo }of the characteristic time of the conductivity curve downstream from the filtration unit coinciding with the instant at which the mathematical estimation function f_norm_est takes on a value of one;synchronizing the upstream and downstream conductivity curves on the basis of the characteristic times t0
_{Cdi }and t0_{Cdo }determined by the upstream and downstream curves to enable a comparison of the respective conductivity values; andcomparing the upstream conductivity curve and the downstream conductivity curve after the respective conductivity curves have been synchronized to determine one or more downstream conductivity values;
wherein the measured values of the downstream conductivity curve Cdo are corrected on the basis of conductivity fluctuations generated in the measured values of the upstream conductivity curve Cdi by computing the deviation that the upstream conductivity curve Cdi does from its mean value over the change in the conductivity, and then adjusting the downstream conductivity curve Cdo in proportion to said deviation.
74. A blood treatment machine comprising:
at least a filtration unit with a first compartment for the circulation of blood and a second compartment for the circulation of the treatment fluid, said first and second compartments being separated by interposing at least a semi-permeable membrane;
means for changing the conductivity of the treatment fluid upstream from the filtration unit;
at least a first sensor installed upstream from the filtration unit and a second sensor installed downstream from the filtration unit, wherein said first sensor measures the conductivity of a process fluid upstream from the filtration unit and said second sensor measures the conductivity of the process fluid downstream from the filtration unit; and
a control unit governing said devices in order to change the conductivity of the process fluid, said control unit being configured to receive conductivity signals from the first and second sensors, the control unit being configured to execute the steps of
75. A method according to
76. A method according to
_{Cdi}+0.5 minutes, and an instant at which the effects of the change in conductivity cease in the same curve, tf_{clr}−0.5 minutes.77. A method according to
78. A method for determining conductivity of a treatment fluid downstream from a filtration unit in blood processing machines, said unit comprising a first compartment for the circulation of blood and a second compartment for the circulation of the treatment fluid, separated from the first compartment by interposing at least a semi-permeable membrane; said method comprising the steps of:
creating a flow of treatment fluid through the second compartment of the filtration unit;
imposing, for a predetermined time interval, a change in the conductivity of the treatment fluid at the inlet of the filtration unit in order thereby to cause an induced conductivity change in the fluid at the outlet of said filtration unit;
measuring a predetermined number of conductivity values Cdo downstream from the filtration unit and belonging to a conductivity curve downstream from the filtration unit, wherein the method further comprises the steps of:
defining at least one interpolating mathematical function for the purpose of estimating the pattern of the conductivity curve Cdo downstream from the filtration unit in an interval of time after the occurrence of the induced conductivity change; wherein the mathematical function has the form:
Cdo_ln_{clr} =Cdi _{step,mean}−sign*exp(c(1)*t+c(2))where c(1) c(2) are coefficients derived from the least squares interpolation of the mathematical function and Cdi
_{step,mean}=inlet conductivity value after the change in conductivity;determining a characteristic measuring time tcalc
_{clr};calculating by means of a control unit the value of the interpolating mathematical function at said characteristic measuring time tcalc
_{clr}, said value representing the conductivity value Cdo2 of the process fluid downstream from the filtration unit after the induced conductivity change, wherein the determination of the characteristic measuring time tcalc_{clr }comprises the following sub steps:estimation of an intermediate time tA
_{clr }representative of a transient due to the induced conductivity change in the fluid, said time tA_{clr }depending on at least a filtration unit volume, blood and treatment fluid flows and the change in the conductivity of the treatment fluid at the inlet of the filtration unit; wherein the intermediate time tA_{clr }is calculated using the function:
unit _{—} f=ln(sign*(Cdi _{step,set} −Cdo)/potential)where potential=Cdi
_{step,mean}−Cdo_{pre,mean};where Cdi
_{step,set}=a value of the known change in conductivity at the filtration unit inlet;where Cdo=conductivity values measured downstream from the filtration unit;
where Cdi
_{step,mean}=inlet conductivity value after the change in conductivity;where Cdo
_{pre,mean}=average outlet conductivity value prior to the change in conductivity;and by performing an interpolation with least squares estimation on the data of an area falling between said function and the x-coordinate time axis in a predetermined time interval, said intermediate time tA
_{clr }coinciding with the instant at which the interpolating function intersects the time axis, the area taking on a value of zero; andcorrection of the intermediate time tA
_{clr }through the addition of a second time term tcbf, which is a function of blood flow, tcalc_{clr }being defined as tcalc_{clr}=tA_{clr}+tcbf, Cdo2 value being the value of the equation at t=tcalc_{clr}.Description The present invention relates to a method for conductivity calculation in a treatment fluid upstream and downstream a filtration unit in apparatuses for the blood treatment. The invention also relates to a method for clearance and fistula flow determination using the above process for conductivity calculation. It is known in the art to use conductivity measures for determination of parameters indicative of the filter efficiency during treatment, i.e. clearance or dialysance, and for determination of patient parameters, such as fistula flow. EP 547025 shows a first method for determining clearance starting from a perturbation of the conductivity of the upstream dialysis liquid which creates corresponding response in the conductivity of the liquid downstream the dialysis unit. Measures of the conductivity allow determination of downstream response and calculation of the clearance. It is also known from EP 658352 an alternative method to calculate conductivity values for clearance calculation a short time perturbation. It is also known to determine fistula flow by making a step like perturbation in the upstream conductivity and reversing the lines in the extracorporeal circuit during the step perturbation. Measuring the conductivities in the spent dialysate across the flow reversal it is possible to arrive at fistula flow determination. While the fistula flow calculation according to the above methods quite acceptable, it would be highly desirable to increase accuracy trying to reduce the time of the step like perturbation. More in general it is a goal of the invention to devise a method for conductivity determination in the spent dialysate upon a perturbation in the upstream liquid, increasing the accuracy, while keeping an acceptable measurement time. It is also an aim of the present invention to render conductivity detections as much as possible independent from the step size, from the operating conditions and from the presence of undesired disturbances or noises. These and other aims besides which shall be made clearer in the course of the following description, are substantially attained by a method for determining the conductivity of a treatment fluid downstream from a filtration unit in blood processing machines, as described in the accompanying claims. Further features and advantages will become more readily apparent from the detailed description of a preferred, but not exclusive, embodiment of a process for determining the treatment fluid conductivity according to the invention. Such description shall be made hereafter with reference to the accompanying drawings, provided purely by way of non-limiting indication: The present invention relates to a technique for determining the conductivity of a treatment fluid downstream from a filtration unit in blood processing machines and also describes one technique of calculating clearance and access flow. The method is based on studying the dialysate outlet conductivity response that follows a rising of the dialysis solution conductivity and a shifting of the blood flow connections to the patient. The response of a dialysis solution conductivity step is dependent on many factors. It is therefore difficult to extract the asymptotic components needed for calculation of the clearance. This is true even more so for the access flow step, since the change in dialysate outlet conductivity, due to the reversal of the blood flow direction, is really small. The algorithm described below has shown to be the one that gives the best results for both clinical data as well as data generated by a computer model. The various variables used in the specification and in the claims later on are below defined in the table 1. When relevant, the time interval from which data shall be extracted and processed for calculating the variable is given. Some of the definition are also illustrated in
The following calculation method is particularly adapted for blood-treatment apparatuses having at least a filtration unit The machine also comprises means for changing the conductivity of the treatment fluid upstream from the filtration unit Obviously the treatment machine also comprises at least a first sensor A control unit From a general point of view, after creating a flow of treatment fluid through the second compartment The step in the Cdi curve is clearly shown in Such a step cause thereby an induced conductivity change in the fluid at the outlet of said filtration unit (see again FIG. After a predetermined time interval following the step in the inlet conductivity the blood flow to the fistula is reversed causing recirculation in the fistula and the consequent change in the conductivity curve downstream from the filtration unit (see the second step in the Cd0 curve— The method allows firstly to determine the conductivity value Cdo2 of the process fluid downstream from the filtration unit after the induced conductivity change used for clearance calculation and then allows to calculate also access flow. Clearance is calculated by studying the first part of the step response curve. The measurement procedure is activated by the operator. Thereafter no changes to the treatment parameters are allowed in order to create stable conditions for the measurement. In a period of three minutes before the known Ultra filtration (UF) calibration, Cdo and Cdi-data are being collected. These data are necessary for the estimation of Cdo1 and Cdi1. In connection to the UF-calibration, in fact at the end of it, a step in Cdi is initiated. After about 1 minute the response in Cdo is beginning show. After an additional time of 5 minutes the operator is prompted to reverse the blood flow direction to the patient. Should the operator not have reversed the flow within 2 minutes, the measurement should be aborted. From the time when having reversed the blood flow direction, it again takes some 1 minute until the effects start to show in the Cdo-curve. Just before the effects start to show we have reached as far in the measurement as to plot the curve that is seen in Fluctuations in Cdi create fluctuations in Cdo. Since we want to study the effects in Cdo of a raise in Cdi it would have been optimal if Cdi had been constant. Of course Cdi is not constant, but one way of “making it appear constant”, is to compute the deviation that Cdi does from its mean value over the pulse, and then adjust the Cdo in proportion to it. Through this, we will expect a Cdo-curve close to the one we would have got if the response in Cdi had been equal to the actual pulse mean value. To be able to perform this adjustment the two curves must be made synchronous. We therefore have to find the starting point of the curves and move one of them to the starting point of the other. The synchronization process then allows to compare the conductivity curves upstream and downstream from the filtration unit after they have been synchronized in order thereby to determine one or more downstream conductivity values. Finding the start of the Cdi pulse, is quite straightforward. It is done by assessing how the area under the step develops (should be an almost straight line), make a line fit to the pulse area “line” and see at what time it has its zero value (tA In other words the characteristic time (t0 The point when Cdi goes back to normal, tf The determination of the characteristic time t0 When finding t0 Prior to 3 a UF calibration was made. As can be seen, the UF calibration will result in a “bump”. The bump might be quite big if, as in this case, there is a big difference between the patient conductivity and the set conductivity. What is shown here is quite extreme, but it shows an important case. We know that the raise in conductivity is not made until the UF calibration is finished. This occurs when the bump is on its way downwards, i.e. at 3. Data prior to this point in time shall therefore not be used. We also know that it will take some minute before the raise in Cdi will start to show in Cdo. Therefore we can actually exclude another half a minute of data after the end of the UF calibration. We do not exclude the full 1 minute since we need to have some margin. After any UF calibration there is always a “recoil effect”, before Cdo returns to the course it had before the UF calibration. This means that we have some data, between 3 and 1 that should not be used either. If we do, we will, in the case described by If the patient conductivity is larger than the set conductivity, the “bump” will go downwards and the recoil effect will accordingly go upwards. This means that the condition above is not enough. In this situation, when having followed the steps above, we would get Cdo-data that has a minimum at 1 ( By excluding these data we have almost solved the problem. We are however not there yet, since we might in fact get the minimum at the “wrong end”. We must therefore first check if there are any points lying below (or above if the step goes downwards) Cdo Furthermore, it can happen that all data are above Cdo The case described by The data that now remains represents the step response and the very first data point of these data could, probably in most cases, with good enough result, be used as t0 In other words the preliminary estimation of the value of the characteristic time of the conductivity curve downstream from the filtration unit is made by determining the average conductivity at the outlet of the filtration unit Cdo Subsequently the measured conductivity values are compared with previously determined average outlet conductivity value Cdo As above stated where the measured conductivity values Cdo exceed the average outlet conductivity value Cdo We shall however undertake some “additional” steps to find an even better t0 We start by creating the natural logarithm function f=ln(sign*(Cdi We then make a least mean square line fit to function f between t=(tRev−1.5 minutes) and t=tRev. This range represents a part of the curve where the transients have died out. The estimation is called Cdo The next step is to make a least mean square line fit to ln(f_norm) in the range 0.2<f_norm<0.8, i.e. the initial part of the curve (different ranges might be used e.g. 0,1:0,9). An estimation of f_norm, f_norm_est, is then given by f_norm_est=exp(c By having performed the selection of data as described above, we know that f_norm=1 corresponds to Cdo=Cdo We have now got the needed t0 values and can start adjusting the data. We start by synchronizing the two curves (i.e. moving the Cdo data so that t0 The mean value of Cdi during the step is calculated. To get the most appropriate mean value we use data between (t0 Also a value representing the pre step Cdo parameter is needed. We will here use a mean value of the data. It is denoted Cdo We are interested mainly in the big variations in Cdi and will therefore filter the signal quite hard. Only data between t=(t0 Now that we have adjusted the data the method further comprises a step of consisting in mathematical computation of the conductivity curve downstream from the filtration unit in order thereby to determine a characteristic time tStartCF beyond which the conductivity curve has stabilized after undergoing the effects of the imposed change in conductivity. Said characteristic time tStartCF is given by the sum of two terms, a first term t In determination of the first term t We will firstly obtain what we call tA The next step is to construct a line going through the points (t0 To t The time tcbf has two uses. The first is adding it to t We choose to make the line fit to data between t=tstartCF Should it not be possible to use data up to t=(tstartCF Cdo2 is the value that Cdo Cdo1 is given by function Cdo Above is described the case where a fixed time of 1.5 minutes is used for fitting a curve to Cdo-data in order to get Cdo2. This gives, as an average, a better value on the effective clearance Ke. However, from a standard deviation of Ke point of view (if possible), it could perhaps be better to use as much data as possible from the step. If this is done we need however to move the calculation point somewhat towards the left since the whole curve and hence also Cdo2 otherwise becomes a bit too high. As shown in Assuming that we got the conductivity value Cdo2 from the first line fit at time t=112.1 min, to get the same Cdo2 value from the second line fit we need to move towards the left, to t=118 min. In the real case, if, for stability reason, we would choose to use more data this would represent the second curve fit. Consequently we should move the calculation point to the left. One choice is to use t0 The access flow is calculated from the step one get when shifting the blood flow to the needles, i.e. blood taken out upstream is shifted with blood entering downstream. This creates a recirculation in the fistula, which affects the efficiency of the dialysis. K The procedure for the access step calculations could theoretically be the same as for the clearance step. However, the noise is making this approach difficult since this step is much smaller than the clearance one. Therefore we need to do somewhat differently. We are going to describe two ways of finding the parameters needed. One that gives a more correct point for calculation of the access flow, but which might result in a larger variation. The second approach gives results which are the other way around. The method for calculating fistula flow generally comprises the step of determining the filter clearance as above described, when reversing the blood flow direction to the fistula and determining, by means of mathematical calculation, an outlet conductivity prior the reversal of the blood flow Cdon; furthermore the method includes the step of determining a conductivity of the outlet process fluid Cdor following the reversal in blood flow and setting or estimating an inlet conductivity Cdi after the imposition of a change in conductivity. If the switching of the blood flow to the fistula is made manually one should choose t0 We want our method to find consistent values of t0 One problem of using derivatives of signals is that they usually become noisy. The first action is therefore to filter Cdo We create the function f_flt=ln(sign*(Cdi By using the f2 How the access flow is calculated is described below. If the switching of the blood flow to the fistula is made automatically, a somewhat better point in time to use for the access flow calculation is tA tA In The access flow is calculated using the expression To get the values of the conductivities we create the function f in the same way as for the clearance step. We make a least mean square line fit to the function for data lying between t=tstartCF Dependent on the situation of manual or automatic reversion of the blood flow, as described above, we use tA The access flow that has now been calculated is the blood water access flow Q The invention achieves important advantages. First of all it is to be noted that the method for determining the conductivity according to the present invention allows to increase the accuracy of calculation of clearance and of access flow. The method is adapted to be used with different blood treatment machines and gives good results for different patients in different conditions. In other words the method is general. The present method allows also to more accurately access a conductivity needed for calculation of the clearance and of access flow by giving better estimation of the time point when the transition effect starts and ends. Finally the conductivity detections are as much as possible independent from the step size, the operating conditions and from the presence of undesired disturbances or noises. Patent Citations
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